WASHINGTON — For public consumption, President Trump planned to use his State of the Union address on Tuesday night to appeal for bipartisan unity. But at a private lunch for television anchors earlier in the day, he offered searing assessments of a host of Democrats.

Mr. Trump dismissed former Vice President Joseph R. Biden Jr. as “dumb,” called Senator Chuck Schumer of New York a “nasty son of a bitch” and mocked Gov. Ralph Northam of Virginia, who he said “choked like a dog” at a news conference where he tried to explain a racist yearbook photo, according to multiple people in the room.

The White House declined to comment on the president’s remarks.

Energized and blunt, Mr. Trump held little back during the lunch at the White House to preview the State of the Union address. As he has in past years, he offered an unvarnished, unscripted view of the political world that went well beyond the heavily vetted speech he delivered to a joint session of Congress and a national television audience.

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He seemed confident about his chances for re-election next year, breaking down the emerging field of possible opponents with scathing assessments and predicting that Democrats would move so far to the left that it would make it easier for him to win a second term.

He said he hoped he would get to run against Mr. Biden. “I hope it’s Biden,” Mr. Trump said. “Biden was never very smart. He was a terrible student. His gaffes are unbelievable. When I say something that you might think is a gaffe, it’s on purpose; it’s not a gaffe. When Biden says something dumb, it’s because he’s dumb.”

He also expressed a desire to take on Senator Elizabeth Warren of Massachusetts, whom he regularly derides with the racially inflammatory nickname of Pocahontas because she has claimed a distant Native American heritage.